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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 6
# Folio 16r, page id 00068051:0031
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Vinit adn
sit formula irrationalisus = fax tabxx + ux + reducendues
ad talem, ubi sub vinculo indeterminata non ascendat ultra gradum rdm
explicando X rationaliter; ita nempe at ex non sit irrationalis. fiat
pu si posset tolli temminus unxi maximus res esset confecta. Sed tunc oportet
valorem ipsius X habere inde terminatam in nominatire de, quo max. pitum
ergo sentemus collere duos terminos infimes sibque X = inZ tnn: a
et fiet ax = nZ3 + 3mmnnzZ + 3 mnt Z + n6: aa
yy B2h
accx =
ad3
+ab mnZZ + 2 ab mmZ + abrt: aa
+aacc inz + aacemn; ac
+ad: aa
Verum hinc patet posse quidem tolli terminum infinium, per n
sed hoc sublato non est in pte ut tollatur penultimus per m,
quia m in eo evanescit
faciamus X = mZ + nn: y+ p habemus nominatorem 1Z+ p
in balore ipsius y. et ita non habemus intenta.
si la
quod si mulliplicemus numeralirem adhuc per Z+ p
ut videamus, an licet enim sic assurgatur ad Z, vider tamen
potent an liceat tollere duos terminos summos
sit ergo _. X = mZ + nn: Z+ p = 0: d, fiel
auyu = a O + ab O0D + acc OD) +ad 3
= a CD + ab 00D) + acc O V + ad 3: 3)
quaeramus teminus summos in a0D est am Z + aBmp
in
+3 amumBZ.
ab edD est, abmmiz tabmmp
+rabmun 33
ac cOD est facemZ Haacemp 23
in ac ad s est ad
R
2
+aaccnn 13)
93
+4ad B Z et X d = Z - nn. d,:, Z-
Ar est constans Ergo hoc casu res nonceder
Ut ergo autios terminos simul tollamus fiet m bmm + cc m + d =0
et p L am + rab mun 1 aaccn: et - p = Sammun + 2 ab mtn pa ce 
e
regulanter,
Hinc sequitur fimmutam quamvis irrationalem simili Methado
Es 19
1
deprimi posse ad inferiorem, et hanc rursus ad inferiorem, atque ita hinc sequibe
formutam quamvis posse ubbi extrahibilem. Hinc sequitur et compositas
reodi posse itales sit enim exempli causa
YEX + Px+q
V  YX pX∞ + qXar + Y aX + 1Xx + ex +d, reddatur primum
una ex partialibus extrahibilis, deinde et altera fiet denique non formula ratio
ncet  lactu suceta i qua arqur petato aotrum tinti
icet.
:aa
O: aa
O. aa
d. O= numZZ L2munZ+n
 2
D.
-Q13piZ3php
ID = 22 + 2pZ + B p
D-
2
2
D- 21 a p ebppi
+p
si estet b4c, -0, finet
u
y= Xa ida
et m = dH et  mm= dd
et M = d3 et fiet
p
=p= 3add Lad + 4d3 
seu p = = pn. d
et x = -dZ + nn :  - nn: d
am + 2 ab mm + zascemtad